The use of a single threshold for deciding on acceptance or rejection in a probabilistic two-way decision-making process is inappropriate when the available information is uncertain or incomplete. Probabilistic three-way decisions use a pair of thresholds to trisect the universe allowing a more effective and sensible decision-making process. Determination of optimal thresholds in the probabilistic three-way decision-making model minimizes the overall uncertainty of the three regions. This assures the quality of trisections and guides to more valuable and accurate decisions. Quality of trisection can be measured with the use of objective functions. In this paper, the optimal pair of thresholds is determined experimentally by using Shannon entropy and chi-square static as objective functions and are analyzed and compared.

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A major challenge in present day data mining is the high dimension of datasets. Because of the high dimensionality of data, feature selection becomes a necessary pre-processing step to data mining, which removes superfluous features and enhances performance of classification. Thus, attribute reduction becomes an important pre-processing step for data mining. The concepts of rough set theory have been successfully used for attribute reduction. Reducts in rough set theory provide a minimal set of attributes preserving the knowledge. Removal of an attribute from a reduct creates information loss. The severity of information loss due to removal of an attribute depends on the significance of that attribute. In many cases, the variation in classification accuracy when an attribute that has negligible significance is removed from a reduct may not be significant. Removal of insignificant attributes is useful when dealing with high dimensional data sets. In this paper, a novel method is proposed to identify attributes with negligible significance which can be removed from a reduct. Experimental results for various datasets are presented. The results prove that the accuracy of classification do not vary much after the removal of the insignificant attributes from the reduct.